Efficient Implementation of Gsm/Gprs Equalizer

1. A method of estimating at least one transmitted MSK symbol by a Viterbi equalizer at a wireless receiver, the transmitted MSK symbols being alternately real and imaginary, the Viterbi states possible at the stages corresponding to real symbols constituting a first set of states, the Viterbi states possible at the stages corresponding to imaginary symbols constituting a second set of states, the method comprising the steps of: a. obtaining only the imaginary parts of the autocorrelation values of the channel impulse response corresponding to a time delay of odd number of stages; b. obtaining only the real parts of the autocorrelation values of the channel impulse response corresponding to a time delay of even number of stages; c. pre-computing an estimated ISI term for all Viterbi states using the real and imaginary parts obtained at steps (a) and (b); d. advancing the Viterbi trellis by a stage comprising the steps of: i. if the transmitted MSK symbol corresponding to the stage is real then performing steps of: 1. pre-processing the received symbol at the stage to obtain a real component representing the received symbol corresponding to the stage; and 2. determining the surviving path for only the first set of states at the stage, using the estimated ISI terms corresponding to the first set of states, the real component representing the received symbol corresponding to the stage and the path metrics of the surviving paths at the previous stage; else performing the steps of: 1. pre-processing the received symbol at the stage to obtain an imaginary component representing the received symbol corresponding to the stage; and 2. determining the surviving path for only the second set of states at the stage, using the estimated ISI terms corresponding to the second set of states, the imaginary component representing the received symbol corresponding to the stage and the path metrics of the surviving paths at the previous stage; ii. determining whether at least one transmitted MSK symbol can be estimated at the stage; and iii. estimating at least one transmitted MSK symbol using the surviving paths at the stage if it is determined that at least one transmitted MSK symbol can be estimated at the stage.

2. The method as recited in claim 1 wherein the step of estimating at least one transmitted MSK symbol using the surviving paths at the stage comprises the steps of: a. selecting a maximum likelihood path from the surviving paths at the stage; and b. analyzing the maximum likelihood path to estimate at least one transmitted MSK symbol.

3. The method as recited in claim 1 wherein the step of determining whether at least one transmitted MSK symbol can be estimated at the stage comprises determining whether the Viterbi trellis has been advanced for a predefined number of stages N.

4. The method as recited in claim 2 wherein the step of analyzing the maximum likelihood path to estimate at least one transmitted MSK symbol comprises tracing back along the maximum likelihood path to the N th previous stage to estimate the transmitted MSK symbol at the N th previous stage.

5. The method as recited in claim 2 wherein the step of analyzing the maximum likelihood path to estimate at least one transmitted MSK symbol comprises tracing back along the maximum likelihood path by previous N stages to estimate the transmitted MSK symbols at the previous N stages.

6. The method as recited in claim 1 wherein the step of determining the surviving path for only the first set of states at the stage comprises, for each state of the first set of states, comprises the steps of: a. obtaining the path metric of the first possible path leading to the state at the stage, using the estimated ISI terms corresponding to the state, the real component representing the received symbol corresponding to the stage and the path metric of the surviving path for the state at the previous stage on the first possible path; b. repeating step (a) for the second possible path leading to the state at the stage; and c. selecting the path having greater path metric as the survivor path to the state at the stage.

7. The method as recited in claim 2 wherein the step of selecting the maximum likelihood path from the surviving paths comprises selecting the surviving path with maximum path metric.

8. The method as recited in claim 6 wherein the step of obtaining the path metric CM n (I n ) of a possible path leading to the state at the stage n comprises calculating CM n (I n ) using the relation CM n ⁡ ( I n ) = CM n - 1 ⁡ ( I n - 1 ) + 2 ⁢ ℜ ⁢ { I n } ⁢ ⁢ ℜ ⁢ { y n } - 2 ⁢ ℜ ⁢ { I n * ∑ m = 1 L ⁢ I n - m * x m } -  I n  2 ⁢ x 0 , where CM n−1 (I n−1 ) is the path metric of the possible path at stage n− 1 , I n denotes the transmitted MSK symbol corresponding to stage n, {I n } denotes real part of the transmitted MSK symbol corresponding to stage n, {y n } is the real component representing the received symbol corresponding to the stage n, x m is the autocorrelation value of the channel impulse response for the time delay of m stages.

9. The method as recited in claim 6 wherein the step of obtaining the path metric CM n (I n ) of a possible path leading to the state at the stage n comprises calculating CM n (I n ) using the relation CM n ⁡ ( I n ) = CM n - 1 ⁡ ( I n - 1 ) + 2 ⁢ ℜ ⁢ { I n } ⁢ ⁢ ℜ ⁢ { y n } - 2 ⁢ ℜ ⁢ { I n * ∑ m = 1 L ⁢ I n - m * x m } , where CM n−1 (I n−1 ) is the path metric of the possible path at stage n−1, I n denotes the transmitted MSK symbol corresponding to stage n, {I n } denotes real part of the transmitted MSK symbol corresponding to stage n, {y n } is the real component representing the received symbol corresponding to the stage n, x M is the autocorrelation value of the channel impulse response for the time delay of m stages.

10. The method as recited in claim 2 wherein the step of determining the surviving path for only the second set of states at the stage, for each state of the second set of states, comprises the steps of: a. obtaining the path metric of the first possible path leading to the state at the stage, using the estimated ISI terms corresponding to the state, the imaginary component representing the received symbol corresponding to the stage and the path metric of the surviving path for the state at the previous stage on the first possible path; b. repeating step (a) for the second possible path leading to the state at the stage; and c. selecting the path having greater path metric as the survivor path to the state at the stage.

11. The method as recited in claim 2 wherein the step of selecting the maximum likelihood path from the surviving paths comprises selecting the surviving path with maximum path metric.

12. The method as recited in claim 1 wherein the step of advancing the Viterbi trellis by a stage comprises considering the stages in the reverse time direction.

13. The method as recited in claim 1 wherein the step of pre-computing an estimated ISI term l for k th Viterbi state comprises calculating l using the relation l = 2 ⁢ ℜ ⁢ { I n * ∑ m = 1 L ⁢ I n - m * x m } , where I n is the transmitted MSK symbol corresponding to stage n, x m is the autocorrelation value of the channel impulse response for the time delay of m stages, and the transmitted MSK symbols {I n−1 , I n−2 . . . , I n−L } correspond to k th Viterbi state.

14. The method as recited in claim 1 wherein the step of pre-processing the received symbol at the stage to obtain a real component {y n } representing the received symbol corresponding to the stage n comprises calculating {y n } using the relation ℜ ⁢ { y n } = ∑ m = 1 L ⁢ { ℜ ⁢ { h m } ⁢ ⁢ ℜ ⁢ { r n - m } - 𝔍 ⁢ { h m } ⁢ ⁢ 𝔍 ⁢ { r n - m } ) , where {h m } is the real part of the m th channel tap, ℑ{h m } is the imaginary part of the m th channel tap, {r n−m } is the real part of the received symbol at the (n−m) th stage, ℑ{r n−m } is the imaginary part received symbol at the (n−m) th stage.

15. The method as recited in claim 1 wherein the step of pre-processing the received symbol at the stage to obtain an imaginary component ℑ{y n } representing the received symbol corresponding to the stage n is performed using the relation 𝔍 ⁢ { y n } = ∑ m = 1 L ⁢ ( 𝔍 ⁢ { h m } ⁢ ⁢ ℜ ⁢ { r n - m } + ℜ ⁢ { h m } ⁢ ⁢ 𝔍 ⁢ { r n - m } ) , where {h m } is the real part of the m th channel tap, ℑ{h m } is the imaginary part of the m th channel tap, {r n−m } is the real part of the received symbol at the (n−m) th stage, ℑ{(r n−m } is the imaginary part received symbol at the (n−m) th stage.

16. A method of estimating at least one transmitted MSK symbol by a Viterbi equalizer at a wireless receiver, the transmitted MSK symbols being alternately real and imaginary, the Viterbi states possible at the stages corresponding to real symbols constituting a first set of states, the Viterbi states possible at the stages corresponding to imaginary symbols constituting a second set of states, a predefined number of transmitted MSK symbols constituting a data burst, the data burst comprising a training sequence as a midamble, the set of symbols transmitted after the midamble constituting a first data set, the set of symbols transmitted before the midamble constituting a second data set, the method comprising the steps of: a. obtaining only the imaginary parts of the autocorrelation values of the channel impulse response corresponding to a time delay of odd number of stages; b. obtaining only the real parts of the autocorrelation values of the channel impulse response corresponding to a time delay of even number of stages; c. pre-computing an estimated ISI term for all Viterbi states using the relation l n = ∑ m = 1 L ⁢ I n - m * x m , where n is the stage for which the estimated ISI term is being calculated, I n is the transmitted MSK symbol corresponding to stage n, and x m is the autocorrelation value of the channel impulse response for the time delay of m stages obtained at step (a) and (b); d. advancing the Viterbi trellis by a stage in the forward time direction for estimating the transmitted MSK symbols of the first data set, the step of advancing the Viterbi trellis by a stage, the advancing comprising the steps of: if the transmitted MSK symbol corresponding to the stage is real then performing steps of: 1. pre-processing the received symbol at the stage to obtain a real component representing the received symbol corresponding to the stage; and 2. determining the surviving path for only the first set of states at the stage, using the estimated ISI terms corresponding to the first set of states, the real component representing the received symbol corresponding to the stage and the path metrics of the surviving paths at the previous stage; else performing the steps of: 3. pre-processing the received symbol at the stage to obtain an imaginary component representing the received symbol corresponding to the stage; and 4. determining the surviving path for only the second set of states at the stage, using the estimated ISI terms corresponding to the second set of states, the imaginary component representing the received symbol corresponding to the stage and the path metrics of the surviving paths at the previous stage; if the transmitted MSK symbol corresponding to the stage is the last symbol of the data burst then performing the steps of: 1. selecting a first maximum likelihood path from the surviving paths at the stage; and 2. tracing back along the first maximum likelihood path to identify the symbols on the first maximum likelihood path as the transmitted MSK symbols of the first data set; and e. advancing the Viterbi trellis by a stage in the backward time direction for estimating the transmitted MSK symbols of the second data set, the step of advancing the Viterbi trellis by a stage, the advancing comprising the steps of: if the transmitted MSK symbol corresponding to the stage is real then performing steps of: 1. pre-processing the received symbol at the stage to obtain a real component representing the received symbol corresponding to the stage; and 2. determining the surviving path for only the first set of states at the stage, using the estimated ISI terms corresponding to the second set of states, the real component representing the received symbol corresponding to the stage and the path metrics of the surviving paths at the previous stage; else performing the steps of: 1. pre-processing the received symbol at the stage to obtain an imaginary component representing the received symbol corresponding to the stage; and 2. determining the surviving path for only the second set of states at the stage, using the estimated ISI terms corresponding to the first set of states, the imaginary component representing the received symbol corresponding to the stage and the path metrics of the surviving paths at the previous stage; if the transmitted MSK symbol corresponding to the stage is the first symbol of the data burst then performing the steps of: 1. selecting a second maximum likelihood path from the surviving paths at the stage; and 2. tracing back along the second maximum likelihood path to identify the symbols on the second maximum likelihood path as the transmitted MSK symbols of the second data set.

17. The method as recited in claim 1 wherein one or more of the steps are embodied in a computer program product.

18. The method as recited in claim 16 wherein one or more of the steps are embodied in a computer program product.

19. A system for equalizing an MSK symbol at a wireless receiver using a Viterbi algorithm, the transmitted MSK symbols being alternately real and imaginary, the Viterbi states possible at the stages corresponding to real symbols constituting a first set of states, the Viterbi states possible at the stages corresponding to imaginary symbols constituting a second set of states, the system comprising: a. means for obtaining only the imaginary parts of the autocorrelation values of the channel impulse response corresponding to a time delay of odd number of stages; b. means for obtaining only the real parts of the autocorrelation values of the channel impulse response corresponding to a time delay of even number of stages; c. means for pre-computing an estimated ISI term for all Viterbi states using the real and imaginary parts of the autocorrelation values; and d. a Viterbi equalizer advancing the Viterbi trellis by a stage, the Viterbi equalizer comprising: i. a pre-processor pre-processing the received symbol at the stage to optionally obtaining a real and an imaginary component representing the received symbol depending on a control signal ii. an add-compare-select unit determining the surviving path optionally for the first set of states and the second set of states depending on the control signal, using the pre-computed estimated ISI terms, the real or imaginary component obtained by the pre-processor, and the path metrics of the surviving paths at the previous stage; iii. a control unit generating a control signal to the pre-processor and the add-compare-select unit depending on the transmitted MSK symbol being real or imaginary; and iv. means for estimating at least one transmitted MSK symbol using the surviving paths at the stage.

20. The system as recited in claim 19 wherein the means for estimating a transmitted MSK symbol using the surviving paths at the stage comprises: a. means for selecting a maximum likelihood path from the surviving paths determined by the add-compare-select unit; and b. means for analyzing the maximum likelihood path to estimate at least one transmitted MSK symbol.

21. The system as recited in claim 20 wherein the means for analyzing the maximum likelihood path to estimate at least one transmitted MSK symbol comprises means for tracing back along the maximum likelihood path to a previous stage to estimate the transmitted MSK symbol at the previous stage.

22. The system as recited in claim 20 wherein the means for analyzing the maximum likelihood path to estimate at least one transmitted MSK symbol comprises means for tracing back along the maximum likelihood path to estimate the transmitted MSK symbols at all stages being traced back.

23. The system as recited in claim 19 wherein the add-compare-select unit comprises: a. means for obtaining the path metric of a possible path leading to a state at a stage, using the pre-computed estimated ISI terms, the real and imaginary component representing the received symbol obtained by the pre-processor, and the path metric of the surviving path for the state at the previous stage on the possible path. b. means for selecting the path having greater path metric as the survivor path for the state at the stage.

24. The system as recited in claim 20 wherein means for selecting a maximum likelihood path from the surviving paths comprises means for selecting the surviving path with maximum path metric.

25. The system as recited in claim 19 wherein the Viterbi equalizer comprises a path memory storing the path metrics of the surviving paths at a stage.

26. The system as recited in claim 19 further comprising a look-up table storing the pre-computed estimated ISI term for all Viterbi states.

27. The system as recited in claim 26 wherein the Viterbi equalizer comprises means for advancing the stages in the reverse time direction using the pre-computed estimated ISI terms stored in the look-up table.